Title:Simultaneous interpretation of $K$ and $B$ anomalies in terms of chiral-flavorful vectors

Abstract: We address the presently reported significant flavor anomalies in the Kaon
and $B$ meson systems such as the CP violating Kaon decay
($\epsilon'/\epsilon$) and lepton-flavor universality violation in $B$ meson
decays ($R_{K^{(*)}},{R_{D^{(*)}}}$), by proposing flavorful and chiral vector
bosons as the new physics constitution at around TeV scale. The
chiral-flavorful vectors (CFVs) are introduced as a 63-plet of the global
$SU(8)$ symmetry, identified as the one-family symmetry for left-handed quarks
and leptons in the standard model (SM) forming the 8-dimensional vector. Thus
the CFVs include massive gluons, vector leptoquarks, and $W',Z'$-type bosons,
which are allowed to have flavorful couplings with left-handed quarks and
leptons, and flavor-universal couplings to right-handed ones, where the latter
arises from mixing with the SM gauge bosons. The flavor texture is assumed to
possess a "minimal" structure to be consistent with the current flavor
measurements on the $K$ and $B$ systems. Among the presently reported
significant flavor anomalies in the Kaon and $B$ meson systems
($\epsilon'/\epsilon$, $R_{K^{(*)}}, {R_{D^{(*)}}}$), the first two
$\epsilon'/\epsilon$ and $R_{K^{(*)}}$ anomalies can simultaneously be
interpreted by the presence of CFVs, the ${R_{D^{(*)}}}$ anomaly is predicted
not to survive, due to the approximate $SU(8)$ flavor symmetry. Remarkably, we
find that as long as both of the $\epsilon'/\epsilon$ and $R_{K^{(*)}}$
anomalies persist beyond the SM, the CFVs predict the enhanced $K^+ \to \pi^+
\nu \bar{\nu}$ and $K_L \to \pi^0 \nu \bar{\nu}$ decay rates compared to the SM
values, which will readily be explored by the NA62 and KOTO experiments, and
they will also be explored in new resonance searches at the Large Hadron
Collider.